Ashley is 16 years older than Gabriela. Twelve years ago, Ashley was 5 times older than Gabriela. How old is Ashley now?
We can use the given information to write down two equations that describe the ages of Ashley and Gabriela. Let Ashley's current age be $a$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $a = g + 16$ Twelve years ago, Ashley was $a - 12$ years old, and Gabriela was $g - 12$ years old. The information in the second sentence can be expressed in the following equation: $a - 12 = 5(g - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to solve our first equation for $g$ and substitute it into our second equation. Solving our first equation for $g$ , we get: $g = a - 16$ . Substituting this into our second equation, we get the equation: $a - 12 = 5($ $(a - 16)$ $ -$ $ 12)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $a - 12 = 5a - 140$ Solving for $a$ , we get: $4 a = 128$ $a = 32$.